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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

When is a right orderable group
locally indicable?


Authors: Patrizia Longobardi, Mercede Maj and Akbar Rhemtulla
Journal: Proc. Amer. Math. Soc. 128 (2000), 637-641
MSC (1991): Primary 20F19; Secondary 06F15, 20F60
Published electronically: October 25, 1999
MathSciNet review: 1694872
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Abstract | References | Similar Articles | Additional Information

Abstract: If a group $G$ has an ascending series $ 1 = G_{0} \leq G_{1} \leq \dots \leq G_{\rho } = G$ of subgroups such that for each ordinal $\alpha ,\ G_{\alpha }\vartriangleleft G$, and $G_{\alpha + 1}/G_{\alpha }$ has no non-abelian free subsemigroup, then $G$ is right orderable if and only if it is locally indicable. In particular if $G$ is a radical-by-periodic group, then it is right orderable if and only if it is locally indicable.


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Additional Information

Patrizia Longobardi
Affiliation: Dipartimento di Matematica e Applicazioni “R. Caccioppoli", via Cintia, Monte S. Angelo, 80126, Napoli, Italy
Email: longobar@matna2.dma.unina.it

Mercede Maj
Affiliation: Dipartimento di Matematica e Informatica, via Salvator Allende, 84081 Baronissi (Salerno), Italy
Email: maj@matna2.dma.unina.it

Akbar Rhemtulla
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: akbar@malindi.math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05534-3
PII: S 0002-9939(99)05534-3
Received by editor(s): March 15, 1998
Published electronically: October 25, 1999
Additional Notes: The third author wishes to thank NSERC for partial financial support.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society